Related papers: Banach neural operator for Navier-Stokes equations

We propose the Factorized Fourier Neural Operator (F-FNO), a learning-based approach for simulating partial differential equations (PDEs). Starting from a recently proposed Fourier representation of flow fields, the F-FNO bridges the…

Neural Operators (NOs) provide a powerful framework for computations involving physical laws that can be modelled by (integro-) partial differential equations (PDEs), directly learning maps between infinite-dimensional function spaces that…

The Koopman operator has entered and transformed many research areas over the last years. Although the underlying concept$\unicode{x2013}$representing highly nonlinear dynamical systems by infinite-dimensional linear…

Koopman operator theory has emerged as a powerful tool for system identification, particularly for approximating nonlinear time-invariant systems (NTIS). This paper considers a network of agents with limited observation capabilities that…

Neural operators are a type of deep architecture that learns to solve (i.e. learns the nonlinear solution operator of) partial differential equations (PDEs). The current state of the art for these models does not provide explicit…

Neural Networks (NNs) have been identified as a potentially powerful tool in the study of complex dynamical systems. A good example is the NN differential equation (DE) solver, which provides closed form, differentiable, functional…

Fourier Neural Operators (FNOs) have emerged as promising surrogates for partial differential equation solvers. In this work, we extensively tested FNOs on a variety of systems with non-linear and non-stationary properties, using a wide…

Analyzing the inner mechanisms of deep neural networks is a fundamental task in machine learning. Existing work provides limited analysis or it depends on local theories, such as fixed-point analysis. In contrast, we propose to analyze…

Bayesian Optimization (BO) is a widely used approach for blackbox optimization that leverages a Gaussian process (GP) model and an acquisition function to guide future sampling. While effective in low-dimensional settings, BO faces…

Temporal distributional shifts, with underlying dynamics changing over time, frequently occur in real-world time series and pose a fundamental challenge for deep neural networks (DNNs). In this paper, we propose a novel deep sequence model…

Koopman operators, since introduced by the French-born American mathematician Bernard Koopman in 1931, have been employed as a powerful tool for research in various scientific domains, such as ergodic theory, probability theory, geometry,…

Accurate modeling and control of autonomous vehicles remain a fundamental challenge due to the nonlinear and coupled nature of vehicle dynamics. While Koopman operator theory offers a framework for deploying powerful linear control…

The Koopman operator is a mathematical tool that allows for a linear description of non-linear systems, but working in infinite dimensional spaces. Dynamic Mode Decomposition and Extended Dynamic Mode Decomposition are amongst the most…

Neural networks have been used to solve different types of large data related problems in many different fields.This project takes a novel approach to solving the Navier-Stokes Equations for turbulence by training a neural network using…

Neural operators have gained recognition as potent tools for learning solutions of a family of partial differential equations. The state-of-the-art neural operators excel at approximating the functional relationship between input functions…

In this work, we propose a meta-learning-based Koopman modeling and predictive control approach for nonlinear systems with parametric uncertainties. An adaptive deep meta-learning-based modeling approach, called Meta Adaptive Koopman…

In this work, we introduce a new class of neural network operators designed to handle problems where memory effects and randomness play a central role. In this work, we introduce a new class of neural network operators designed to handle…

Ensemble simulations of high-dimensional flow models (e.g., Navier Stokes type PDEs) are computationally prohibitive for real time applications. Neural operators enable fast inference but are limited by costly data requirements and poor…

An important application of neural networks to scientific computing has been the learning of non-linear operators. In this framework, a neural network is trained to fit a non-linear map between two infinite dimensional spaces, for example,…

Inverse problems in fluid dynamics are ubiquitous in science and engineering, with applications ranging from electronic cooling system design to ocean modeling. We propose a general and robust approach for solving inverse problems in the…